Plasmons in coupled electron-hole double quantum wells

We calculate the plasmon excitations in InAs/GaSb double quantum wells (QWs) coupled by tunneling. In this system the valence band of the GaSb layer overlaps with the conduction band of the InAs layer, and a tunneling gap is formed in the single particle energy spectrum due to the coupling between electrons in the InAs layer and holes in the GaSb layer. The plasmon spectrum is calculated within the random phase approximation for different positions of the Fermi level. We demonstrate that in general the plasmon spectrum consists of two branches, optical and acoustic. Both modes strongly depend on the position of the Fermi level. An optical mode exists for any position of the Fermi level above or below the tunneling gap. There is an acoustic mode only when the Fermi level is in the range of energies where the unperturbed electron and hole bands overlap, excluding the tunneling gap. When the Fermi level is positioned in the tunneling gap both modes disappear. This gap in the plasmon spectrum is unique for semimetallic InAs/GaSb double QWs and does not have any analog in the GaAs-based double QWs. The plasmon dispersion law and its dependence on the Fermi level position are analyzed numerically as well as analytically in the long wavelength limit, neglecting retardation effects.